Bücher der Reihe Applied Mathematical Sciences

A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations.

The idea for this book was developed in the seminar on problems of con tinuum mechanics, which has been active for more than twelve years at the Faculty of Mathematics and Physics, Charles University, Prague.

An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds.

The investigation of wave packets and their bi furcations is very interesting, and useful theoretically and in practice, not only in geophysical fluid dynamics, which is the field to which the theory is being applied here, but also in other fields in mathematics and the natural sciences.

Presents a discrete in time-space universal map of relative dynamics that is used to unfold an extensive catalogue of dynamic events not previously discussed in mathematical or social science literature.

This text was developed over a three year period of time (1971- 1973) from a variety of notes and references used in the presentation of a senior/first year graduate level course in the Division of En gineering at Brown University titled Linear System Theory.

For readers primarily interested in appli- tions a recommended minimum course consists of Chapter I, the sections of Chapters II, III, and IV so recommended in the introductory sec tions of those chapters, and all of Chapter V.

The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans formations.

This monograph would never have come to fruition without the enthu siasm and drive of Dave Eberly-a former student, now collaborator and coauthor-and without several significant breakthroughs in our understand ing of the phenomena of blowup or thermal runaway which certain models discussed possess.

Finite element methods have become one of the most versatile and powerful methodologies for the approximate numerical solution of PDEs. This book is a thorough yet concise guide to the theory and practice of least-square finite element methods.

This book presents an account of theories of flow in porous media which have proved tractable to analysis and computation. In particular, the theories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail.

Perturbation methods have always been an important tool for treating nonlinear differential equations. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction.

Since there are several excellent books on stability theory, the author selected some recent topics in stability theory which are related to existence theorems for periodic solutions and for almost periodic solutions.

With contributions by numerous experts

With its mathematically rigorous presentation, this book is a detailed treatment of the approach from an inverse problems point of view. It is geared towards graduate students and researchers in applied mathematics and can serve as a text for graduate courses.

This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University.

These notes originate from a one semester course which forms part of the "Math Methods" cycle at Brown. Although asymptotic analysis is now enjoying a period of great vitality, these notes do not reflect a research oriented course. In practice, the means for a rigorous analysis are not always available.

The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations.

This book is the result of two courses of lectures given at the University of Cologne in Germany in 1974/75. When writing this book, we had considerable help and many discussions with H. Springer-Verlag showed a lot of patience and under standing during the course of the production of the book.

This book examines the basic mathematical properties of solutions to boundary integral equations and details the variational methods for the boundary integral equations arising in elasticity, fluid mechanics and acoustic scattering theory.

An operator theoretic approach to robust control analysis for linear time-varying systems, with the emphasis on the conceptual similarity with the H control theory for time-invariant systems.

Applied Mathematics is the art of constructing mathematical models of observed phenomena so that both qualitative and quantitative results can be predicted by the use of analytical and numerical methods.

A linear optimization problem is the task of minimizing a linear real-valued function of finitely many variables subject to linear con straints;

The scattering of acoustic and electromagnetic waves by periodic sur faces plays a role in many areas of applied physics and engineering. Trains of surface waves on the oceans are natural diffraction gratings which influence the scattering of electromagnetic waves and underwater sound.

Stratified fluids whose densities, sound speeds and other parameters are functions of a single depth coordinate occur widely in nature. The purpose of this monograph is to develop from first principles a theory of sound propagation in stratified fluids whose densities and sound speeds are essentially arbitrary functions of the depth.

They are mainly concerned with regularity theory for obstacle problems, and with the dam problem, which, in the rectangular case, is one of the most in teresting applications of Variational Inequalities with an obstacle.

The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. This book serves as an entree for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations.

My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.